- #1

omar yahia

- 9

- 0

the homogeneous solution is y

_{h}= c

_{1 }e

^{-x}+ c

_{2 }e

^{x}+ c

_{3}e

^{2x}

the particular solution is y

_{p}=y

_{1}u

_{1}+y

_{2}u

_{2}+y

_{3}u

_{3}

as u

_{1}=∫ (w

_{1}g(x) /w) dx , u

_{2}=∫ (w

_{2}g(x) /w) dx , u

_{3}=∫ (w

_{3}g(x) /w) dx

w =

|y

_{1}y

_{2}y

_{3}|

|y'

_{1}y'

_{2}y'

_{3}|

|y''

_{1}y''

_{2}y''

_{3}|

when i choose y

_{1}, y

_{2}, y

_{3}to be e

^{-x},e

^{x},e

^{2x}i get an answer ,

but when i change the arrangement (like: e

^{x},e

^{-x},e

^{2x})

i get another different answer !

so , i have two questions

1 is it normal to have different results when changing who is y

_{1}, y

_{2}, y

_{3}, or am i doing something wrong?

2 if it is normal , does that mean i can have too many different particular solutions , just by changing who is y

_{1}, y

_{2}, y

_{3}?